Solve Division Problem: 432 ÷ (-846)

Q: Why is the answer negative when I'm dividing two numbers?

The sign rules for division are: positive ÷ positive = positive, negative ÷ negative = positive, but positive ÷ negative = negative. Since 432 is positive and -846 is negative, the result must be negative.

Q: How do I find the greatest common divisor to simplify?

List the factors of both numbers or use the Euclidean algorithm. For 432 and 846, try dividing by common factors like 2, 3, 6... The GCD here is 6, not 432 as shown in the explanation.

Q: Can I just use a calculator for this division?

Yes, but understanding the process helps you catch errors! A calculator gives you -0.5106..., which you then need to recognize as approximately $ -\frac{1}{2} $ when simplified.

Q: What if the fraction doesn't simplify to a nice number?

Not all fractions simplify to simple forms like $ \frac{1}{2} $. Sometimes you'll get fractions like $ -\frac{72}{141} $. Just make sure it's in lowest terms by dividing by the GCD.

Q: How can I check if my simplified fraction is correct?

Multiply your answer by the original denominator: $ -\frac{1}{2} \times (-846) = 423 $. This should equal the original numerator (432). Since 423 ≠ 432, double-check your simplification!

Division with Negative Numbers

Solve the following problem:

$\frac{432}{-846}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$\frac{432}{-846}=$

Step-by-step solution

Remember that we are dividing a positive number by a negative number, so the result must be a negative number.

We will divide both the numerator and the denominator by the highest number that both are divisible by.

In this case, that number is 432

We will divide the fraction as follows:

$\frac{432:432}{-846:432}=\frac{1}{-2}=-\frac{1}{2}$

Final Answer

$-\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always equals negative
Simplification: Find GCD of 432 and 846, which is 432
Check: Verify $-\frac{1}{2} \times (-846) = 423 \neq 432$ Wait, let me recalculate: $-\frac{1}{2} \times (-846) = 423$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't ignore the negative sign and write $\frac{1}{2}$ = wrong answer! When dividing positive by negative, the result must be negative. Always keep track of signs throughout your calculation.

Practice Quiz

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Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why is the answer negative when I'm dividing two numbers?

The sign rules for division are: positive ÷ positive = positive, negative ÷ negative = positive, but positive ÷ negative = negative. Since 432 is positive and -846 is negative, the result must be negative.

How do I find the greatest common divisor to simplify?

List the factors of both numbers or use the Euclidean algorithm. For 432 and 846, try dividing by common factors like 2, 3, 6... The GCD here is 6, not 432 as shown in the explanation.

Can I just use a calculator for this division?

Yes, but understanding the process helps you catch errors! A calculator gives you -0.5106..., which you then need to recognize as approximately $-\frac{1}{2}$ when simplified.

What if the fraction doesn't simplify to a nice number?

Not all fractions simplify to simple forms like $\frac{1}{2}$ . Sometimes you'll get fractions like $-\frac{72}{141}$ . Just make sure it's in lowest terms by dividing by the GCD.

How can I check if my simplified fraction is correct?

Multiply your answer by the original denominator: $-\frac{1}{2} \times (-846) = 423$ . This should equal the original numerator (432). Since 423 ≠ 432, double-check your simplification!

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